Naively, I have regarded the expression sich nicht ausschließen lassen as something that one would typically apply to one hypothesis out of several (especially if this hypothesis looks particularly unlikely), and would translate it as cannot be ruled out.
In summary, I have understood the phrase as an acknowledgement of possibility that nevertheless still conveys a considerable measure of doubt.
I just came across the phrase sich nicht ausschließen lassen in a context that contradicts this understanding of it.
The original source is the book Duden Redewendungen, on p. 321:
sich nicht von der Hand weisen lassen/nicht von der Hand zu weisen sein: offenkundig, nicht zu verkennen sein, sich nicht ausschließen lassen: ...
Going only by the other alternative definitions that precede it in this citation, I would conclude that sich nicht ausschließen lassen was more or less synonymous with offenkundig [sein] ("to be obvious") and nicht zu verkennen sein ("impossible to miss, unmistakable")1.
Contrary to my original translation, these alternative translations convey the impossibility of doubt.
How is this contradiction to be resolved?
1 Implicit in this interpretation is the assumption that, in the context of a definition appearing in a work of reference, comma-separated alternatives are to be taken as "more or less synonymous".